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A car with a mass of 980 kg is initially traveling east toward an intersection with...

A car with a mass of 980 kg is initially traveling east toward an intersection with a speed of vc = 19.6 m/s and a 1500 kg pickup is traveling north toward the same intersection. The car and truck collide at the intersection and stick together. After the collision, the wreckage (car and truck) moves off in a direction of 35.0° above the x-axis. Determine the initial speed of the truck and the final speed of the wreckage.

a.   initial speed of the truck    ? m/s
b.    final speed of the wreckage ? m/s

Solutions

Expert Solution

Consider Vt as the initial speed of the truck and V as the final speed of the wreckage.

a)
Equating momentum along the x-axis,
Mc * Vc = (Mc + Mt) * V * cos(35) ...(1)
Where Mc is the mass of the car and Mt is the mass of the truck.

Equating momentum along the y-axis
Mt * Vt = (Mc + Mt) * V * sin(35) ...(2)

(2) / (1) gives,
(Mt * Vt) / (Mc * Vc) = tan(35)
Vt = [(Mc * Vc) tan(35)] / Mt
= [(980 * 19.6) * tan(35)] / 1500
= 8.97 m/s

b)
Substituting values in equation (1),
980 * 19.6 = (980 + 1500) * V * cos(35)
19208 = 2031.5 * V
V = 19208 / 2031.5
= 9.46 m/s

genius_generous answered 2 years ago
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